File systems are the way that a computer organizes its programs, boot procedures, etc. It determines how information is stored (Wikipedia can get way more in depth than me about things like block size and whatnot) on the system.

Ext3 is a common linux file system, Windows used to be FAT but now is primarily NTFS, then you get into network file systems (NFS, CIFS, NTFS) which are ways of mounting a hard drive on a remote computer (say your desktop) as a sorta pseudo-folder on something like your phone.

I have my movies and music folder shared on one of my systems, and I can use a free program called CIFS manager (in the android marketplace) as a front-end to mount those network shares and stream content while I'm laying in bed. I made it through at least half of BSG and Caprica thanks to this.